Bell numbers, log-concavity, and log-convexity

Nobuhiro Asai, Izumi Kubo, Hui-Hsiung Kuo

Let $\{b_k(n){\}}_{n=0}^{\infty }$ be the Bell numbers of order $k$. It is proved that the sequence $\{b_k(n)/n!{\}}_{n=0}^{\infty }$ is log-concave and the sequence $\{b_{k}(n)\}_{n…